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A034305
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Zeroless nonprimes that remain nonprime if any digit is deleted.
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12
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14, 16, 18, 44, 46, 48, 49, 64, 66, 68, 69, 81, 84, 86, 88, 91, 94, 96, 98, 99, 122, 124, 125, 126, 128, 142, 144, 145, 146, 148, 152, 154, 155, 156, 158, 162, 164, 165, 166, 168, 182, 184, 185, 186, 188, 212, 214, 215, 216, 218, 221, 222, 224, 225, 226, 228
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
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MATHEMATICA
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npQ[n_]:=!PrimeQ[n]&&FreeQ[IntegerDigits[n], 0]&&AllTrue[FromDigits/@ Table[Drop[IntegerDigits[n], {k}], {k, IntegerLength[n]}], !PrimeQ[#]&]; Select[Range[10, 300], npQ](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 19 2021 *)
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PROG
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(Haskell)
a034305 n = a034305_list !! (n-1)
a034305_list = filter f $ drop 9 a052382_list where
f x = a010051' x == 0 &&
(all (== 0) $ map (a010051' . read) $
zipWith (++) (inits $ show x) (tail $ tails $ show x))
-- Reinhard Zumkeller, May 10 2015
(PARI) is(n)=my(d=digits(n)); if(#d<2 || vecmin(d)<1 || isprime(n), return(0)); for(i=0, #d-1, if(isprime(fromdigits(vecextract(d, 2^#d-1-2^i))), return(0))); 1 \\ Charles R Greathouse IV, Jun 25 2017
(Python)
from sympy import isprime
def ok(n):
if n < 10 or isprime(n): return False
s = str(n)
return "0" not in s and not any(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
print([k for k in range(229) if ok(k)]) # Michael S. Branicky, Jan 15 2023
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CROSSREFS
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Subsequence of A052382.
Cf. A034302, A034303, A034304, A010051.
Sequence in context: A053425 A178071 A177982 * A091898 A061365 A327822
Adjacent sequences: A034302 A034303 A034304 * A034306 A034307 A034308
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KEYWORD
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base,nonn,nice
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AUTHOR
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David W. Wilson
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EXTENSIONS
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Definition corrected by T. D. Noe, Apr 02 2008
Single-digit terms removed again by Georg Fischer, Jun 21 2021
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STATUS
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approved
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